首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube tha
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube tha
admin
2022-10-18
65
问题
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube that joins the 2 points.If a cube has edges of length 4 centimeters,what is the surface distance,in centimeters。between the lower left vertex on its front face and the upper right vertex on its back face?
选项
A、
B、
C、
D、
E、
答案
B
解析
The left figure below shows a cube with edge length 4, where P is the lower left vertex on its front face and Q is the upper right vertex on its back face. It is clear that the shortest path on the surface between P and Q consists of a path on the front face joined to a path on the top face, or a path on the front face joined to a path on the right face. In fact, each of these two approaches can be used in essentially the same way to give a path from P to Q, whose length is the surface distance between P and Q. To simplify the exposition, we will consider the case where the surface distance is the length of a certain path P
F
on the front face plus the length of a certain path P
T
on the top face.
The middle figure below shows the top face of the cube lifted about 45 degrees, and the right figure below shows only the front and top faces of the cube after the top face has been lifted 90 degrees. Since rotations of the top face about this "hinge" do not change the length of any path on the front face or on the top face, this rotation by 90 degrees will not change the length of Pp or the length of P
T
and hence this rotation will not change the sum of the lengths of P
F
and P
T
.
In the right figure below, the shortest path from P to Q is the dashed segment shown in the figure. Moreover, the length of this dashed segment is the surface distance between P and Q because if P
F
and P
T
did not correspond to portions of this dashed segment on the front and top faces, respectively, then the sum of the lengths of P
F
and P
T
would be greater than the length of the dashed segment, since the shortest distance between P and Q in the right figure below is the length of the line segment with endpoints P and Q.
From the discussion above, it follows that the surface distance between P and Q is the length of the dashed segment in the right figure, which is easily found by using the Pythagorean
theorem:
The correct answer is B.
转载请注明原文地址:https://kaotiyun.com/show/CktO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Doyouknowinsurance(保险)?Buyinginsuranceisameansbywhichpeoplecanprotectthemselves【C1】______largelosses.Protection
Icanhardly______thedifferencebetweenthesetwowords.
Birth,marriageanddeath:thesearethegreatesteventsinhumanlife.Manythings,goodandbad,canhappentousinourlives
Icannottellthe()differencebetweenthetwins.
Concerningmoneyoranythingelse,conflictsbetweenhusbandandwifeusuallyreflectapowerstruggle.Conflictsbetweenparen
WeallknowthatDNAhastheabilitytoidentifyindividualsbut,becauseitisinherited,therearealsoregionsoftheDNAstr
Inanoldtownlivedamerchant.Heearnedhugeprofitsbyfairmeansandfoul(恶劣的).Withmoreprofitsflowingin,hebecamemor
Allthefollowingcasesareon-the-jobsmokingexceptthat______.Inthesecondpartofthepassage,theauthorsuggestsbannin
Allthefollowingcasesareon-the-jobsmokingexceptthat______.Accordingtothepassage,on-the-jobsmokingaffectsanemplo
Ourpreferencesforcertaincolorsare______accordingtothepassage.Whichofthefollowingcouldbethemostsuitabletitle
随机试题
恩格斯在谈到巴尔扎克的《人间喜剧》时说,“从这里所学到的东西,比从当时所有职业的历史学家、经济学家和统计学家那里学到的全部东西还要多”。这说明了艺术具有______功能。()
男性,55岁,2周前体检发现左肺上叶肿块,直径约3cm,边界较清楚。入院手术切除后病理诊断为结核瘤。肿块中央部分为
男性,32岁,既往有胃病史。近一周来常感上腹部不适,4小时前突发上腹部剧烈疼痛,伴有恶心、呕吐。查体:腹部压痛、肌紧张,肝浊音缩小。X线检查可见膈下游离气体。首先考虑
1998年试题【试题要求】1.任务描述图示木夹板门(图2.3—1)按指定的剖面线位置及剖视方向,绘出构造节点详图,包括与240mm砖墙及过梁的关系,要求构造合理。2.设计任务与构造要求(1)图示木夹板门,中悬亮窗,下部有百叶,双面胶合板门。(
宋代东京汴梁城的特点是()。
根据第五次全国人口普查的结果,我国男性占总人口的51.63%,女性占总人口的48.37%,那么人口的性别比为( )。
资料(一)威达电子电工股份有限公司是2005年在深交所上市的公司,主要从事磁性材料、半导体材料、电动机、电热设备工业自动化装置、电子电工产品制造设备的研发、生产和销售,母公司为科威股份有限公司(以下简称科威公司)。威达股份于2014年1
约公元前2070年,()建立了我国第一个奴隶制王朝夏朝。
下列情形构成挪用公款罪的是()。
Arapidmeansoflong-distancetransportationbecameanecessityfortheUnitedStatesassettlementspreadfartherwestward.F
最新回复
(
0
)